Optical communication systems

ABSTRACT

A receiver, transmitter, and photon counting detector for use in an optical communication link are disclosed. Also disclosed are methods of communicating using the transmitter, the receiver, and the photon detector.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit under 35 U.S.C. Section 119(e) ofthe following co-pending and commonly-assigned U.S. applications:

-   U.S. Provisional Patent Application No. 62/289,608, filed Feb. 1,    2016, by William H. Farr, entitled “BALANCED GEIGER-MODE AVALANCHE    PHOTODIODE DETECTOR FOR BINARY-POLARIZATION-SHIFT-KEYING OPTICAL    COMMUNICATIONS” (CIT 7436-P);-   U.S. Provisional Patent Application No. 62/300,240, filed Feb. 26,    2016, by Kenneth S. Andrews, William H. Farr, Andre Wong, and Meera    Srinivasan, entitled “OPTICAL BEACON ACQUISITION AND TRACKING USING    UP/DOWN COUNTING ALGORITHMS”; (CIT 7457-P) and-   U.S. Provisional Patent Application No. 62/319,491, filed Apr. 7,    2016, by William H. Farr, entitled “REDUCED POWER/COMPLEXITY    POLARIZATION SHIFT KEYED TRANSMITTER FOR OPTICAL COMMUNICATIONS    LINKS” (CIT 7492-P);

which applications are incorporated by reference herein.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT

The invention described herein was made in the performance of work undera NASA contract NNN12AA01C, and is subject to the provisions of PublicLaw 96-517 (35 USC 202) in which the Contractor has elected to retaintitle.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to methods and devices for opticalcommunication.

2. Description of the Related Art

(Note: This application references a number of different publications asindicated throughout the specification by one or more reference numbersin brackets, e.g., [x]. A list of these different publications orderedaccording to these reference numbers can be found below in the sectionentitled “References.” Each of these publications is incorporated byreference herein.)

Optical communication technology offers the promise of data rates thatare significantly higher than those provided by conventionalradio-frequency-based technology. For deep-space applications, powerefficient communications is possible in part due to the large effectivepower gain from narrow optical beamwidths. Consequently, a necessarycomponent of optical communication systems is highly accurate and stablelaser beam pointing.

In order to establish and maintain an optical link, accurate uplink anddownlink pointing must be performed in the presence of spacecraft motionand disturbances. Disturbance suppression can be achieved through acombination of passive isolation to reduce mechanical coupling betweenthe spacecraft and flight terminal platform, and active cancellation ofpointing errors through platform steering and downlink beam steering viaa fine steering mirror. Local reference sensors such as inertialreference units may be utilized to provide highly accurate informationfor active disturbance cancellation, but increase mass and power on theflight terminal, and do not provide a pointing reference to the Earth.In order to minimize mass on the spacecraft transceiver, the Deep SpaceOptical Communication (DSOC) project at the Jet Propulsion Laboratoryuses an uplink beacon transmitted from the ground terminal to provide areference spot position that may be tracked by the flight terminal. 1 Byestimating the uplink signal position, the flight terminal platformattitude may be adjusted and the point-ahead angle for downlinktransmission may be calculated and implemented. Furthermore, an uplinkbeacon can also carry command and configuration data. By using a singlephotodetector array for both pointing and communications, rather than amore conventional architecture consisting of separate detectors fortracking and communications, beam alignment errors and optical losses aswell as overall system complexity may be minimized. A photon countingarray possesses the best combination of sensitivity and bandwidth forthese purposes. Signal processing algorithms for uplink spatialacquisition and tracking, parameter estimation, and command telemetryprocessing must be therefore be developed in order to simultaneouslysupport tracking and communications for the deep-space optical link.

SUMMARY OF THE INVENTION

The present disclosure describes a transmitter, comprising apolarization maintaining optical fiber having a slow axis and a fastaxis; a fiber optic coupler comprising a first coupler input, a secondcoupler input, and a coupler output, wherein the coupler output iscoupled to the optical fiber; a first laser connected to the firstcoupler input, wherein a first polarization axis of light emitted fromthe first laser is aligned to the slow axis; a second laser connected tothe second coupler input, wherein a second polarization axis of thesecond laser is aligned to the fast axis; and a circuit comprising firstinput, a second input, a third input, a fourth input, a first output anda second output.

The optical fiber outputs the electromagnetic radiation having the firstpolarization axis representing a first binary state and emitted from thefirst laser, when the first output outputs a signal switching the firstlaser on in response to the first input receiving a clock signal and thesecond input receiving a data signal representing the first binary statein a data stream. The optical fiber outputs the electromagneticradiation having the second polarization axis representing a secondbinary state and emitted from the second laser, when the second outputoutputs a signal switching the second laser on in response to the thirdinput receiving the clock signal and the fourth input receiving a datasignal representing the second binary state in the data stream.

The present disclosure further describes a receiver, comprising a firstphotodiode connected to a non-inverting output; a second photodiodeconnected to an inverter, wherein the inverter is connected to anon-inverting output; a bias input resistively coupled to thephotodiodes; an over-biasing input capacitively coupled to thephotodiodes; and an output connected to the non-inverting output and theinverting output.

The output sums a first signal at the non-inverting output with a secondsignal at the inverting output when the first photodiode outputs thefirst signal to the non-inverting output in response to a firstelectromagnetic signal received on the first photodiode, an overbiasingvoltage applied to the overbiasing input, and a bias voltage applied tothe bias input; and/or the inverter outputs the second signal to theinverting output, the second signal formed by inverting the photodiodesignal received from the second photodiode in response to a secondelectromagnetic signal received on the second photodiode, theoverbiasing voltage applied to the overbiasing input and the biasvoltage applied to the bias input. The first signal at least partiallycancels the second signal when the first photodiode receives the firstelectromagnetic signal and the second photodiode receives the secondelectromagnetic signal while the bias voltage and the overbias voltageare applied.

The present disclosure further describes signal processing algorithmsfor optical uplink beacon acquisition, centroiding, and parameterestimation, using a photon-counting detector array. Descriptions of theuplink beacon modulation and flight terminal detector array concept wereprovided, along with statistical models of the detector output,including blocking. Monte Carlo simulation and laboratory test resultsusing a commercial 32×32 photon counting camera were evaluatedparametrically, showing how uplink centroiding accuracy varies withbackground conditions for realistic system parameters. The resultsdemonstrate that the DSOC acquisition and tracking concept using asingle photon counting detector array is capable of achieving the highacquisition probabilities and sub-microradian centroiding accuracyneeded for e.g., deep space optical links or other optical communicationsystems.

The transmitters and receivers described herein can be used in freespace optical communication data links, for example.

BRIEF DESCRIPTION OF THE DRAWINGS

Referring now to the drawings in which like reference numbers representcorresponding parts throughout:

FIG. 1 illustrates a mode-locked-laser plus polarization modulatortopology, according to one or more embodiments of the present invention;

FIG. 2 illustrates modeled Bit Error Rate (BER) for infinite (blue)versus measured (red) BER Polarization Extinction Ratio (PER), whereinusing a commercial LiNbO3 modulator resulted in only 6 dB PER with modelocked laser pulses, versus measured 16.5 dB PER before the modulator(performance is thus degraded by >8 dB at 10-3 BER);

FIG. 3 illustrates a polarization modulator for a mode locked laser(MLL) using a LiNbO3 optical switch, wherein the λ/2 element represents90° polarization rotation (note: replacing this element with a delayline creates a PPM-2 modulator);

FIG. 4 illustrates polarization modulation using a pair of gain switcheddiode lasers, according to one or more embodiments of the invention,wherein the output from a simple 5V logic gate can be converted to therequired short electrical drive pulse by a low power step recovery diodecircuit;

FIGS. 5A and 5B depicts examples of balanced GmAPD connection, accordingto embodiments of the present invention;

FIG. 6 illustrates a BPolSK GmAPD receiver according to one or moreembodiments of the present invention;

FIG. 7 illustrates BPolSK receiver analog signal output using thecircuit of FIG. 6;

FIG. 8A illustrates a space transceiver and FIG. 8B illustrate a deepspace optical communications flight terminal pointing and trackingconcept according to one or more embodiments;

FIG. 9A-9C shows an uplink nested modulation signal structure, whereinFIG. 9A shows the beacon sync pattern (square wave), FIG. 9B shows a lowrate command channel (PPM 2 and 2 guard slots), and FIG. 9C shows a highrate data channel (PPM 8 and 4 guard slots);

FIG. 10A-10C shows detector/readout pixel blocking, wherein FIG. 10Ashows poisson photon arrival process and avalanche photodiode (APD) deadtime, FIG. 10B shows detected photoelectron events with Read outIntegrated Circuit (ROIC) frame interval T_(f), and FIG. 10C shows ROICoutput timestamp events.

FIG. 11 shows unblocked and blocked photoelectron count statistics forsignal and background slots, showing histograms from blocking simulationand Gaussian blocked count model;

FIG. 12A shows beacon slot average intensity and statistics, whereinFIG. 12 A shows 2=PPM+2=ISGT average beacon intensity envelope and FIG.12B shows 2−PPM+2−ISGT modulated intensity beacon slot clock offset;

FIG. 13 shows a block diagram of Matlab uplink signal processingsimulation;

FIG. 14A and FIG. 14B show the probability of missed detection for theuplink beacon signal as a function of integration time in seconds (FIG.14A), and background flux over detector array in counts per second (FIG.14B), wherein the signal flux is 125000 counts per second (˜4.6 pW/m²beacon irradiance at the flight terminal) with 0.0087 cm² sr micronearth radiance;

FIG. 15A and FIG. 15B show analytically calculated uplink centroidestimation error using modified square-law statistics in the absence ofdetector blocking, shown as a function of beacon position within±0.5-pixel of tracking subwindow crosshairs: RSS bias (FIG. 15A) and RSSjitter (FIG. 15B);

FIG. 16A-16B shows RSS bias and jitter as a function of integration timefor modified square-law and up-count beacon centroiding, with andwithout blocking (FIG. 16B);

FIG. 17A-17B show RMS fraction estimation error as function ofintegration time slot timing offset (FIG. 17A), and signal counts persymbol (FIG. 17B);

FIG. 18 shows a laboratory photon counting detector array testbed;

FIG. 19 shows measured centroid X-coordinate vs. uplink spotdisplacement across detector array;

FIG. 20A-20B shows a 32×32 detector array FPGA output with uplinkbeacon, downlink signal, and Earth emulation, showing total detectedcounts over 17 ms (FIG. 20A) and modified square-law statistics over 17ms (FIG. 20B);

FIG. 21 shows laboratory testbed centroid estimation results for 32×32single photon counting detector array, shown as a function of Earth fluxper pixel, and compared with simulation model, wherein FIG. 21A showsposition estimate in pixels and FIG. 21B shows RMS jitter in ura;

FIG. 22 illustrates a method of fabricating a transmitter;

FIG. 23 illustrates a method of fabricating a receiver; and

FIG. 24 illustrates a method of fabricating a photon counting detector;

FIG. 25 illustrates a camera comprising a computer connected to anarray; and

FIG. 26 illustrates a processing environment for use with one or moreembodiments.

DETAILED DESCRIPTION OF THE INVENTION

In the following description of the preferred embodiment, reference ismade to the accompanying drawings which form a part hereof, and in whichis shown by way of illustration a specific embodiment in which theinvention may be practiced. It is to be understood that otherembodiments may be utilized and structural changes may be made withoutdeparting from the scope of the present invention.

Technical Description I. First Example: A Mode Locked Laser forNoise-Limited Optical Communications

1. R⁴ Range Capacity Loss

For an optical communications signal, when the average received signalpower, Ps, is at least about a factor of e/2 (e=2.71828 . . . ) over thenoise power, Pb, (either extrinsic noise or internal photodetectornoise), the communications capacity, C, (bits per second) isproportional to the signal power, Ps. For space optical communications,this implies a data rate that scales as the distance between thetransmitter and receiver (=‘range’, R) squared (R²). However, when noisepower dominates, the capacity C scales as Ps²/Pb. In this regime, datarate scales as R⁴, and the high data rate advantage of opticalcommunications that results from a narrower transmit beam are quicklylost.

2. Acquisition

Before a received signal can be decoded, it first must be ‘acquired’from the background. If the average signal power, Ps, is lower than theaverage noise power, Pb, there must be a way to ‘filter out’ excessnoise to determine the spatial, temporal, and carrier frequency locationof the signal. For ‘pulse-position modulated’ (PPM) optical signalencoding, which trades bandwidth for photon efficiency in opticalcommunications, the peak power per communications symbol is increased bya factor N, where N is the number of time bins per communicationssymbol. If M of N bins are used to encode data, log-base-2 of M bits areencoded per signal. The remaining non-data bins are herein designated G.The increase in peak power (factor of N) aids signal acquisition byallowing the instantaneous signal power to be above the averagebackground power.

Acquisition can be achieved by correlation on a fixed pattern, such asthe lack of signal in the G bins, or by a fixed data sequence, or asingle symbol that repeats at a fixed interval (‘pilot tone’). In noiselimited optical communications, a background power dependent signalpower threshold exists below which acquisition cannot occur, and datacannot be recovered.

3. Modulation Bandwidth

Increasing N, corresponding to increasing modulation bandwidth B(proportional to 1/N), increases both C and aids acquisition. However,modulation bandwidths above about 1 GHz require significantly morecomplicated control circuitry (and additional components), withconventional technology limits presently in the 10 GHz range.

Higher modulation bandwidths also require higher power in controlelectronics due to the energy required to charge and discharge circuitcapacitances through real impedances. Higher complexity and higher powerare negative attributes for space optical communications.

4. Mode-Locked Laser Transmitter Implementation

FIG. 1 illustrates a transmitter comprising a mode-locked-laser 100emitting light comprising mode locked pulses 102 to a polarizationmodulator 104, wherein the polarization modulator 104 modulates thelight with data 106 and outputs the modulated light to a fiber opticpower amplifier 108.

Use of a mode-locked laser enables a very high effective N with minimumcomplexity and power.

A mode-locked laser utilizes a non-linear inter-cavity element togenerate a fixed rate train of narrow pulses (5 ps or less, typical,corresponding to >200 GHz modulation bandwidth), most commonly at pulserepetition frequencies (PRF) in the 20 to 120 MHz range, althoughrepetition rates below 1 MHz and above 10 GHz have been demonstrated.

In one embodiment, communications requires data encoding on the fixedpulse train carrier. One method would be to put the mode-locked laseroutput into a switched set of optical delay lines, creating PPM symbols.Another method would be to use a mode-locked laser with a linearlypolarized output and add a variable polarization rotation controlelement at the output. For M polarization states, log-base-2 M bits canbe encoded.

With a polarization-modulated mode-locked laser, the output pulse trainoccurs at a single fixed repetition rate. Initial acquisition is aidedby the narrow temporal spectrum and high peak power. Once acquired, allof the background noise outside the single data slot of the symbol canbe rejected. In the noise limited regime, C now is proportional to Ps/(BPb). Doubling the bandwidth B doubles the data rate in this regime. Inpractice, the limit on B may be limited by detector timing resolution,versus the pulse width of the mode-locked laser output.

The use of the mode-locked laser, versus a conventional pulse-carvedcontinuous wave laser, allows optical communications links to beestablished in background noise regimes where the signal could not beacquired using conventional modulation schemes.

Very high modulation bandwidth is an inherent feature of the lasersource, versus the complexity and high ancillary power consumption ofmulti-GHz (or multi-hundred-GHz) modulation required in the conventionalscheme. With the mode-locked laser the required modulate rate occursonly at the symbol (=PRF) rate, a factor of N lower than theconventional scheme.

The mode-locked laser modulation scheme allows simplified opticalfiltering before the receiver photodetector. For a conventionalon-off-keyed optical system, the minimum required optical bandwidth ison the order of ten times the modulation bandwidth. However, opticalfilters narrower than a few-hundred GHz are difficult to fabricate withsimultaneous high transmission in the ‘pass’ band and high rejection outof band, and often have severe field-of-view restrictions which prohibituse with large telescopes desired for space optical communications. Forinstance, with an optical carrier at 1550 nm (about 200 THz), astate-of-the-art filter for a 5 m telescope has a 0.17 nm bandwidth,about 22 GHz, with about 80% transmission efficiency. For a 1 Mb/s link,this represents a factor of about 2000 times more background noise intothe system than required by the signal bandwidth. In contrast, a 5 psmode-locked laser system could use a filter with ten times greaterbandwidth, and over 95% transmission efficiency. Assuming a 50 ps timingresolution photodetector and binary modulation at a 1 MHz PRF, anadditional noise factor rejection of (1,000,000 ps/50 ps)=20,000 isobtained after detection, for a 2000 times increase in noise rejectionover the narrower optical filter.

5. Example Applications, Advantages, and Improvements

The new mode-locked laser source and modulation scheme has benefits tocubesat optical communications, lander/rover Direct-to-Earthcommunications, lander/rover to orbiter proximity link operations, andoptical trunkline communications beyond Jupiter. It also has potentialDoD/IC applications for low-probability-of intercept communications andhigh data rate battlefield communications. The mode-locked laser schemecan also fulfill commercial building to building high data rate linkapplications by enabling optical communications under common high-lossconditions such as rain, fog, and smog.

The conventional pulse-carved continuous wave laser scheme has been wellstudied to apply to high-data rate trunk-lines for space opticalcommunications out to perhaps Jupiter range, but does not readily scaledown to either large range (beyond Saturn) or low data rate applicationssuch as cubesat optical communications and Mars rover direct-to-Earthcommunication due to the Pb limited transition to a R⁴ data ratescaling. A simple way of viewing this relation would be to state thatwhile with a conventional pulse-carved continuous wave laser it ispossible to build an optical telecommunications system with over tentimes the data rate performance of an equivalent mass and powerradio-frequency (RF) telecommunications system, the converse is nottrue: you cannot implement the RF telecommunications rate with a 1/10thmass and power optical communications system. Using the mode-lockedlaser source, the latter statement no longer holds.

The narrow pulses and fixed PRF structure inherent with the mode-lockedlaser modulation scheme also simplifies optical ranging schemes, and cansupport millimeter resolution optical ranging for improved spacecraftnavigation. New performance domains in post-Newtonian astrophysics,‘light’ science, and planetary studies are feasible using themode-locked laser in space applications.

II. Second Example: Reduced Power and Complexity Polarization ShiftKeyed Transmitter for Optical Communications Links

1. Introduction

As discussed in section I, polarization modulation of a fixed-rateoptical pulse train is advantageous for establishing opticalcommunications links under high loss and high optical backgroundscenarios. Theoretical analysis and laboratory demonstrations have beenperformed that show the benefits for Mars surface direct-to-Earth, deepspace optical communications cubesats, and ground links in the presenceof inclement weather. Realizations include the optical transmittersolution comprising a mode-locked laser and polarization modulatordescribed in section I (schematically depicted in FIG. 1) and afunctional system utilizing a bulk crystal polarization modulatordescribed above. However, a bulk crystal modulator requires severalhundred volts of drive voltage, which becomes problematic for megabitper second data rates as this translates into many watts of powerrequired for just the modulator alone, independent of the desiredoptical transmit power, which may be less than one watt!

To reduce size, weight, and power, a fiber-optic implementation can beconsidered; however, as shown in FIG. 2, large group velocity dispersionfor the broad band few-picosecond mode locked laser pulses effectivelyprecludes the use of lithium niobate as used in common commercialmodulators, instead requiring expensive/customized modulators in amaterial such as gallium arsenide.

As depicted in FIG. 3, it is possible to utilize lithium niobateswitches 300 coupled with polarization controllers 302 and fiber-opticcouplers, but such an implementation becomes much more complicated anddifficult to stabilize over ambient temperature variations, and such asystem features a minimum 6 dB transmission loss due to the inputbeamsplitter 304. In any of the above described fiber-optic modulatorcases, modulator power consumption is still high, on the order of a wattfor megabit per second data links.

1. Transmitter Example

FIG. 4 illustrates a novel modulator scheme comprising two gain switcheddiode lasers 400, 402 coupled to orthogonal polarization inputs 404, 406of a polarization maintaining fiber-optic coupler 408, with thepolarization axis of one laser 400 being aligned to the “slow” axis of apolarization maintaining fiber 410, and the polarization axis of thesecond laser 402 being aligned to the “fast” axis of a polarizationmaintaining fiber 410. As the two polarizations are separate opticalmodes, they may be combined with theoretically zero loss into a single(spatial) mode output fiber 410, herein presumed to also be polarizationmaintaining. To produce the modulated output, one diode 400 is pulsed torepresent a binary “zero”, while the other laser 402 is pulsed torepresent a binary “one”. The modulation rate can be at a fixedfrequency, yielding an output identical to the mode-locked-laserfollowed by a polarization modulator, or it can now incorporate variablepulse spacings to take advantage of modulation schemes such as pulseposition modulation to achieve higher bits-per-photon link efficienciesthat is possible with just binary polarization modulation alone.

In one or more embodiments, the nominal output pulse energies of themodulator may typically be in the picojoule range, which may be too lowfor many desired operational scenarios. In embodiments requiring higheroutput pulse energies and higher average output powers, the output fromthe polarization-maintaining fiber optic coupler is followed by aconventional polarization-maintaining fiber optic amplifier 412 toachieve watt level average output powers 414.

Thus, more generally, FIG. 4 illustrates a transmitter comprising apolarization maintaining optical fiber 410 having a slow axis and a fastaxis; a fiber optic coupler 404 comprising a first coupler input 404, asecond coupler input 406, and a coupler output 416, wherein the coupleroutput 416 is coupled to the optical fiber 410; first (e.g., gated)laser 400 connected to the first coupler input 404, wherein a firstpolarization axis of light or electromagnetic radiation emitted from thefirst laser 400 is aligned to the slow axis; a second (e.g., gated)laser connected to the second coupler input 406, wherein a secondpolarization axis of electromagnetic radiation or light emitted from thesecond laser 402 is aligned to the fast axis; a circuit 418 comprisingfirst input 420, a second input 422, a third input 424, a fourth input426, a first output 428 and a second output 430. The optical fiber 410outputs the electromagnetic radiation having the first polarization axisrepresenting a first binary state 432 (e.g., 0) and emitted from thefirst laser 400, when the first output 428 outputs a signal switchingthe first laser 400 on in response to the first input 420 receiving aclock signal 434 and the second input 420 receives a data signalrepresenting the first binary state 432 in a data stream 436. Theoptical fiber 410 outputs the electromagnetic radiation having thesecond polarization axis representing a second binary state 438 andemitted from the second laser 402, when the second 430 output outputs asignal switching the second laser 402 on in response to the third input424 receiving the clock signal 434 and the fourth input 426 receiving adata signal representing the second binary state 438 in the data stream436.

In the embodiment shown in FIG. 4, the circuit comprises a logic circuitcomprising a first AND gate having the first input 420, second input 422and the first output 428, and the second AND gate having the third input424, fourth input 426, and the second output 430, wherein the secondinput 422 is an inverting input. However, other logic circuits may beused.

2. Advantages and Improvements

A pair of gain-switched diode lasers with polarization maintainingfiber-coupled outputs combined with a low-loss (<3 dB) polarizationmaintaining fiber optic coupler yields a modulation solution with only10's of milliwatts average power dissipation, versus watts for theseparate laser plus modulator solution.

Furthermore, unlike the mode-locked-laser optical transmitter, thisconfiguration allows easy implementation of pulse position modulationcombined with polarization modulation for higher bits per-photonefficiency when allowed for lower loss and background noise opticalcommunications scenarios A diode laser can naturally generate a linearlypolarized output state. Gain-switching of a diode laser is awell-established technique to directly generate optical output pulses ofa few 10's of picoseconds from longer (nanosecond scale) electricalpulses. In a gain-switched configuration the diode laser is biased wellbelow threshold, for instance on the order of one milliampere, and ashort electrical pulse drives the diode laser well above threshold, forinstance on the order of 80 milliamperes. The initial gain of the diodelaser is very high, and the result is a very short optical pulse,similar to a Q-switched pulse from a gain modulated crystal laser.Before the diode laser can settle down to a steady-state condition withcontinuous optical output, the electrical drive pulse is removed,resulting in a single optical pulse per electrical input pulse, with theoptical pulse being much shorter than the electrical drive pulse.

Moreover, the optical transmitter topology described in FIG. 4 hasfurther advantages over a mode-locked-laser plus polarization modulatorfor optical communications under high loss and high backgroundscenarios:

(1) Pulse-to-pulse timing is now set by an external electronic circuit,versus the physical laser cavity length that sets a fixed pulserepetition frequency in the mode locked laser. This enables (a) dynamicpulse rates to optimize data transmission rate under different loss andbackground conditions, and (b) data encoding using time bin modes, suchas pulse position modulation.

(2) Optical modulators are implemented with materials that all exhibitan optical frequency dependent index of refraction, which results in adifferent propagation delay through the system as a function of opticalfrequency (i.e., color). The result is “group velocity” dispersion whichresults in pulse spreading. This is especially problematic for the broadbandwidth associated with picosecond pulses (order of several angstroms)desired for the high loss/high background optical communications links,resulting in a very poor extinction ratio in the specific case of apolarization modulator. The “Ping-Pong” laser scheme, using one laser torepresent binary zero, and the other to represent binary one, removesthe separate modulator element, thus eliminating the problem. Inaddition, the optical combining element, the polarization maintainingfiber-optic coupler, has minimal dispersion over many nanometers ofbandwidth, and does not contribute to any significant pulse broadening.

III. Example 3: Photodiode Detectors forBinary-Polarization-Shift-Keying Optical Communications

As discussed above, binary-polarization shift keying (BPolSK) modulationof a mode-locked laser is a method to establish an opticalcommunications link under high-loss/high-background conditions. Photoncounting direct detection of the polarization demodulated signal is nearcapacity-achieving. However, the operational efficiency of the link canbe severely limited by the saturation characteristics of Geiger-ModeAvalanche Photodiodes (GmAPD) that are common and attractive for use asphoton counting detectors.

1. Example Receiver

FIG. 5A illustrates a circuit in a receiver, wherein the circuitcomprises two Geiger Mode Avalanche Photodiodes (GmAPDs) 500, 502 withmatched breakdown voltages and junction capacitances biased in parallelfrom a common voltage source through independent current limitingresistors R1, R2, which typically would have a value greater than onekiloOhm. For the case of applying the bias Vbias at the GmAPD 500, 502cathode, the bias will be positive. The bias voltage Vbias would be setto slightly below the breakdown voltage. Overbias pulses Vovr from acommon pulsed low impedance (50 Ohm, typical) source are applied throughparallel AC coupling capacitors C1, C2. For positive bias GmAPD read-outcan be taken from the anodes through parallel transformers T, with oneend of each winding connected to the GmAPD 500, 502 anode, and the otherconnected to ground. The output windings of the transformers areconnected such that one non-inverted and one inverted output are summed.The output sum point (OUT) then is inputted to an amplifier chain with atypical 50 Ohm input impedance. Capacitive feedthrough of the over-biaspulses is naturally cancelled in this configuration, and a photondetection event on one detector will create a positive going pulse,whereas a photon detection event on the other detector will create anegative going pulse. Simultaneous detection events would cancel,creating no detectable output for that over-bias pulse.

One or more embodiments of the invention are not limited to the use oftransformers. More generally, the non-inverted and inverted outputsallowing cancellation can be achieved by using circuit comprising aninverting circuit or inverter, including, but not limited to,transformers.

FIG. 5B illustrates a circuit comprising a first photodiode 506connected to a non-inverting circuitry, circuit elements/components 508having a non-inverting output 510; a second photodiode 512 connected toan inverter or inverter circuit 514, wherein the inverter 514 comprisesan inverting output 516; a bias input Vbias resistively coupled to thephotodiodes 506; an over-biasing input Vover capacitively coupled to thephotodiodes; an output 518 connected to the non-inverting output 510 andthe inverting output 516. The output 518 sums a first signal at thenon-inverting output 510 with a second signal at the inverting output516 when (1) the first photodiode 506 outputs the first signal to thenon-inverting output 510 in response to a first electromagnetic signalreceived on the first photodiode 506, an overbiasing voltage Vovrapplied to the overbiasing input, and a bias voltage Vbias applied tothe bias input; and/or (2) the inverter 514 outputs the second signal tothe inverting output 516, the second signal formed by inverting thephotodiode signal received from the second photodiode 512 in response toa second electromagnetic signal received on the second photodiode 512,the overbiasing voltage Vovr applied to the overbiasing input and thebias voltage applied Vbias to the bias input.

The first signal at least partially cancels the second signal when thefirst photodiode receives the first electromagnetic signal and thesecond photodiode receives the second electromagnetic signal while thebias voltage and the overbias voltage are applied.

In one or more embodiments, the photodiodes have substantiallysimilar/same circuit characteristics (e.g., substantially similar straycapacitance and inductance). In one embodiment, the photodiodes have thesame breakdown voltage. In another embodiment, the photodiodes havedifferent breakdown voltages.

FIG. 6 illustrates an embodiment of a BPolSK receiver wherein theoptical signal is collected by a receiver telescope 600 and an opticalfilter BPF passes only the modulated optical signal frequencies. Apolarization-sensitive beamsplitter PBS splits the received BPolSKsignal into two orthogonal beams, which are independently focused ontoseparate GmAPD detectors 500 and 502 or 506 and 512 in the circuits ofFIG. 5A or FIG. 5B. The detectors 500, 502, 606. The circuits of FIGS.5A and 5B are also connected to bias and pre-amps 602, 604. The summedoutput OUT or 518 from FIG. 5A or FIG. 5B is then input to a polaritysensitive time-to-digital converter 606, for instance, which wouldcapture the time-of-arrival for each detected photon event, for instanceassigning a positive going pulse as equivalent to a binary ‘1’, and anegative going pulse as equivalent to a binary ‘0’. The converter 606 isconnected, e.g., with a USB connection, to a personal computer PC.

The synchronous over-biasing of the GmAPD detectors at the laser pulserepetition frequency minimizes detected noise photons. The seriesconnection of two GmAPDs, one on each port of a polarizing beamsplitter(PBS), combined with opposite polarity driving of the over-biasvoltages, (a) negates the charge feedthrough that occurs due to thedV/dT of the bias source across the GmAPD capacitance, and (b)automatically cancels the detected photon count output in the event ofthe error condition of simultaneous detection of a photon at each outputport of the PBS (i.e., two total). The overall effect is to reduce thetotal number of photons detected by maximizing the number of rejectednoise photons, thus mitigation both GmAPD saturation, other GmAPDimperfections such as after-pulsing, and reducing the processing load onthe data receiver.

FIG. 7 illustrates an output from the system of FIG. 6, wherein positivegoing pulses represent detection of a ‘p’ polarized photon, and negativegoing pulses represent detection of an ‘s’ polarized photon. Residualover-bias pulse feedthrough from junction capacitance mismatch isevident as the small residual sine wave component of the output.However, the single photon detection events are readily thresholded fromthis background noise.

Further information on one or more embodiments of the receiver can befound in reference [9].

2. Advantages and Improvements

The balanced detection scheme minimizes the amount of avalanche chargeflowing through the GmAPD junction, with the benefit of reducing trappedcharge in the devices. Reduced trapped charges means reduced “hold-off”time for the GmAPDs. Hold-off time is required to allow trapped chargesto thermally de-trap, otherwise a charge which de-traps during anover-bias period would create a false detection event. As an example,for an InGaAs on InP GmAPD, the required holdoff time can be reducedfrom over one microsecond to less than ten nanoseconds. As a detectorcannot detect a photon arrival event during the hold-off time, theimpact is greatly improved dynamic range (=count rate) capability. Thisconfiguration is a natural match to BPolSK, which requires twodetectors, one for each orthogonal polarization.

IV. Example 4: Photon Counting Detector Array

1. System Overview and Modeling of a Transceiver Embodiment

The deep-space optical communications flight transceiver [1] relies uponuse of a modulated uplink beacon in order to assist downlink pointingand provide uplink command and data links.

FIG. 8A illustrate a space transceiver according to one or moreembodiments of the invention, comprising telescope optics 800 receivinga beacon 802 from the earth 804 and transmitting a downlink beam 806with a point ahead angle 808 taking into account motion 810 of theearth, retro mirror 812, fine pointing mirror 814, and focal plane array816 receiving the beacon 802.

FIG. 8B illustrates a deep space optical communications flight terminalpointing and tracking concept according to one or more embodiments,comprising the focal plane array 816 outputting a full frame image 818(for acquisition), performing a tracking process 820 using the fullframe image using input from transmitter (tx) spot centroiding 822 andbeacon centroiding 824. The tracking process 820 outputs to a pointingcontrol 826 and an uplink receiver 828 outputs data 830 and receivesinput from beacon centroiding 824.

As shown in FIGS. 8A and 8B, a single aperture for both transmit andreceive beams simplifies boresight alignment issues and enablescontinuous monitoring of the downlink point-ahead angle by imaging bothuplink and downlink signals onto one common focal plane array (FPA) ofsingle-photon-counting detectors, which is used for uplink acquisitionand tracking, downlink point-ahead verification, and uplink datadetection. The FPA converts the uplink photons into attitude informationbased upon the spatial distribution of photons on the detector pixels,and into temporal information via time of arrival data that is used torecover the pulse-position modulated uplink data. The major FPA signalprocessing operations are

-   -   Uplink beacon detection and acquisition: Scanning of the flight        transceiver platform to detect and coarsely determine the uplink        beacon position.    -   Uplink beacon tracking: Fine estimation and control of the        uplink beacon position.    -   Downlink point-ahead verification: Position estimation of the        retro-reflected portion of the downlink laser to verify the        angular offset between the received beacon and the downlink        transmitted beam.    -   Uplink data demodulation: Timing synchronization, parameter        estimation, and data decoding.

2. Uplink Beacon Signal Example

In one or more embodiments, the uplink signal is a nested modulationformat that contains a low-bandwidth command channel and an optionalhigher rate data channel. The inner data modulation consists of higherorder pulse position modulation (PPM), while the low rate outer commandmodulation consists of 2-PPM with two intersymbol guard-time (ISGT)slots [2] (see FIG. 9A-9C showing the transmitted signal 900). If theoptional high rate data channel is included, a block of higher order PPMsymbols (with ISGT) is sent in one of two time intervals of durationT_(c), which are followed by two additional time intervals of durationT_(c) with no signal, thereby creating the 2−PPM+2−ISGT command symbolof duration 4T_(c). If the high rate data is not included, then the2−PPM+2−ISGT with slot duration T_(c) is implemented directly. In eithercase, the average intensity envelope of the combined modulation layersis a square wave that forms a beacon signal whose alternating patternmay be exploited for background rejection, [3] signal acquisition andtracking. Here, it is assumed that the higher rate data channel is notimplemented.

3. Detector Output

In one embodiment, the flight detector consists of a square array ofGeiger mode avalanche photodiode (APD) detectors. [4, 5] Each detectorpixel in the array is a single-photon-counting detector that outputs anelectrical pulse in response to a photon arrival. When operating inGeiger mode, the APD must be quenched after each photon event and thenheld disarmed for a recovery period, introducing a dead time into thedetection process. The result is that photons arriving after the initialphoton arrival and before the end of the dead time interval cannot bedetected. This blocking effect limits the output count rate of thedetector and reduces the effective detection efficiency. The recoverytime, or dead time, is typically an adjustable quantity. The outputcount rate is also limited by the readout frame rate; the readoutintegrated circuit [6] (ROIC) bonded to the APD array outputs atimestamp corresponding to each detected photon arrival pulse, and thistimestamp output is gated so that at most one timestamp per pixel isproduced for each readout frame interval of duration T_(f).Consequently, for each pixel, only the first photon arrival detected inany frame interval gives rise to an output timestamp, or count. Theflight detector blocking model is illustrated in FIG. 10A-10C, wheresome incident photon arrivals are undetected due to the APD dead time τ,and others go undetected due to the ROIC frame limit. In one applicationdescribed herein, the APD dead time is on the same order as the frametime T_(f), so in order to simplify analysis we combine the two effectsinto a single non-paralyzable blocking model with blocking time τ.

For the signal processing functions listed in section 2, it issufficient to know the number of photon counts over various timeintervals rather than the high resolution timestamp values. In theabsence of detector blocking time, the number of detected photon eventsis modeled as a Poisson process in which the probability of detecting kevents over a time interval of duration T is given by

$\begin{matrix}{{P\left\lbrack {{X(T)} = k} \right\rbrack} = {\frac{\left( {\lambda \; T} \right)^{k}}{k!}e^{{- \lambda}\; T}}} & (1)\end{matrix}$

where X(T) is the number of detected counts over an interval of durationT and λ is the average photon arrival rate. Once blocking is considered,the blocked detected count process X_(bl)(T) is no longer Poisson, butmay be approximated as Gaussian distributed [7] with mean and variance

$\begin{matrix}{{{E\left\lbrack {X_{bl}(T)} \right\rbrack} \approx \frac{\lambda \; T}{1 + {\lambda \; \tau}}},{{{Var}\left\lbrack {X_{bl}(T)} \right\rbrack} \approx \frac{\lambda \; T}{\left( {1 + {\lambda \; \tau}} \right)^{3}}},\mspace{11mu} {{{for}\mspace{14mu} \tau} < {T.}}} & (2)\end{matrix}$

FIG. 11 shows histograms of slot count statistics collected fromsimulations of the detector output for a case with mean signal countsper symbol

K _(s)

λ_(s) T _(sym)=7

and mean background counts per slot of

K _(b)

λ_(b) T _(slot)=16.

The probability mass functions of the unblocked Poisson count processesfor the signal and non-signal slots are shown, along with correspondinghistograms for the simulated blocked process with τ/T_(slot)=0.03. TheGaussian model for the blocked probability mass function is alsoplotted, demonstrating that it is a good approximation to the simulatedprocess. The inventors observe that the effect of blocking is to reducethe mean of the signal slot (which contains signal plus background) from23 to 13, and that of the background-only slot from 16 to 11. Thevariance of the blocked probability mass functions are also reduced. Asthe number of incident background photons increases to the point atwhich the detector is saturated (a count always detected in every ROICoutput frame), the blocked signal and background slot countdistributions move closer together and further to the right, botheventually reaching the value T_(slot)/τ, resulting in losses in spatialtracking and data demodulation.

4. Algorithms

Here the focus is upon algorithms for spatial signal detection andtracking using the beacon sync pattern, as well as signal parameterestimation. Signal processing for the demodulation and decoding of thetransmitted uplink data is not addressed here. For spatial tracking, theobjective is to estimate the position of the uplink beacon spot upon theFPA in order to provide an accurate reference for pointing the downlinkbeam. This position estimate must have sub-microradian accuracy. In thepresence of high background fluxes, the accuracy of the positionestimate is compromised. For example, the traditional centroidalgorithm, which in the limit is the maximum likelihood positionestimate, will produce an estimate that is biased towards the center ofmass of the Earth. In order to obtain an unbiased position estimate, ourapproach is to perform the centroiding on a set of statistics that havebeen modified to effectively subtract out the contribution frombackground photons. By alternately incrementing and decrementing twophoton arrival counters (“up-down counting”) that are offset byone-quarter of the square wave period, [3] one or more embodiments ofthe present invention construct pixel statistics for detecting signalpresence in the absence of temporal synchronization of the counters withthe received signal. This leads to a faster spatial acquisition andtracking sequence.

5. Background Subtraction

The average transmitted slot intensity is shown in FIG. 12A-12B for the2-PPM signal with 2 ISGT slots. The flight detector array readout framesare clocked at a multiple of the transmitted slot rate, so that theflight electronics receive multiple samples per transmitted slot. It isassumed that there is a timing offset of δT_(slot)=(k+ε)T_(slot) betweenthe transmitted and receiver symbol clocks, where kε{0, 1, 2, 3} and0≦ε<1, and that the clocks have no significant frequency offset or driftover the duration that an estimate is made. For any given pixel, thesampled version of the received signal consists of slot counts obtainedby summing the number of valid timestamps corresponding to detectedphotoelectron counts over each slot duration. These counts are thenalternately added and subtracted at twice the symbol frequency over N2-PPM+2-ISGT symbols to form “up-down” counter statistics. This processcan be equivalently viewed as accumulating the counts over N2−PPM+2−ISGT symbols into one of four slot count bins denoted by thestatistics X₀, X₁, X₂, and X₃. More explicitly, if {x(n)} is the seriesof slot counts, then

$\begin{matrix}{{X_{m} = {\sum\limits_{n = 0}^{N - 1}{x\left( {{4n} + m} \right)}}},\mspace{14mu} {m \in \left\{ {0,1,2,3} \right\}},} & (3)\end{matrix}$

In the absence of blocking, assuming that k=0, the means and variancesof the accumulated slot statistics are

E[X ₀]=Var[X ₀ ]=Nλ _(b) T _(slot)+2Nλ _(s) T _(slot)  (4)

E[X ₁]=Var[X ₁ ]=Nλ _(b) T _(slot)+2N(1−ε)λ_(s) T _(slot)  (5)

E[X ₂]=Var[X ₂ ]=Nλ _(b) T _(slot)  (6)

E[X ₃]=Var[X ₃ ]=Nλ _(b) T _(slot)+2Nελ _(s) T _(slot),  (7)

wo up-down counter statistics U and V, offset in quadrature, arecalculated for each detector pixel as

U=X ₀ +X ₁ −X ₂ −X ₃  (8)

and

V=X ₀ −X ₁ −X ₂ +X ₃  (9)

Additionally, an up-counter that simply accumulates all of the countsover N symbols is formed for each pixel, and is denoted by

S=X ₀ +X ₁ +X ₂ +X ₃  (10)

For general values of the integer part k of the symbol offset, theexpected values of the counter outputs are given by

$\begin{matrix}{{{E\lbrack U\rbrack} \equiv {\mu_{1}\left( {k,\varepsilon,\lambda_{s}} \right)}} = \left\{ \begin{matrix}{4{N\left( {1 - \varepsilon} \right)}\lambda_{s}T_{slot}} & {k = 0} \\{{- 4}\; N\; \varepsilon \; \lambda_{s}T_{slot}} & {k = 1} \\{{- 4}{N\left( {1 - \varepsilon} \right)}\lambda_{s}T_{slot}} & {k = 2} \\{4N\; \varepsilon \; \lambda_{s}T_{slot}} & {k = 3}\end{matrix} \right.} & (11) \\{{{E\lbrack V\rbrack} \equiv {\mu_{2}\left( {k,\varepsilon,\lambda_{s}} \right)}} = \left\{ \begin{matrix}{4N\; \varepsilon \; \lambda_{s}T_{slot}} & {k = 0} \\{4{N\left( {1 - \varepsilon} \right)}\lambda_{s}T_{slot}} & {k = 1} \\{{- 4}N\; \varepsilon \; \lambda_{s}T_{slot}} & {k = 2} \\{{- 4}{N\left( {1 - \varepsilon} \right)}\lambda_{s}T_{slot}} & {k = 3}\end{matrix} \right.} & (12) \\{{E\lbrack S\rbrack} = {4{N\left( {\lambda_{b} + \lambda_{s}} \right)}T_{slot}\mspace{25mu} {\forall{k.}}}} & (13)\end{matrix}$

In the absence of blocking, the variances of these random variable areall equal to each other, and given by

Var[U]=Var[V]=Var[S]=4N(λ_(b)+λ_(s))T _(slot)≡σ²  (14)

From (11) and (12), it is observed that the expected values of the twoup-down counters U and V are functions of the signal flux λ_(s) but notthe background flux λ_(b), and may therefore be used to estimate theposition of the signal while the effect of background is mitigated. Forease of analysis, the distribution of U, V, and S is approximated to beGaussian with the means and variances given above, which is a reasonableassumption for the integration times involved. The indices (i,j) areadded to the counter notation to denote the pixel statistic from thei-th column and j-th row of the detector array. It may be shown thatconditioned upon the values k, ε, λ_(si,j), and λ_(bi,j),

Cov[U _(i,j) ,V _(i,j) |k,ε,λ _(s) _(i,j) ,λ_(b) _(i,j) ]=0, ∀i,j  (15)

Here, λ_(si,j) and λ_(bi,j) are the mean signal and background fluxesfor pixel (i,j). It is also assumed for analytical purposes thatequation (15)=

Cov[V _(i,j) ,V _(l,m) |k,ε,{λ _(s)},{λ_(b)}]=Cov[S _(i,j) ,S _(l,m)|k,ε,{λ _(s)},{λ_(b)}]=0, ∀(i,j)≠(l,m).  (16)

This last assumption in (16) does not generally hold for realdetectors—in practice there is measurable crosstalk between pixelsleading to non-zero covariance. Also note that Cov[U_(i,j), S_(i,j)] andCov[V_(i,j), S_(i,j)] are nonzero.

6. Signal Detection and Acquisition

The joint probability density function of the statistics U_(i,j),V_(i,j), and S_(i,j) may be formed using the Gaussian approximations andmeans and variances given in Section 3.1, and the sufficient statisticfor signal detection and parameter estimation may then be derived. Asthis is mathematically intensive, a heuristic decision statisticsobtained from inspection of the expressions in Section 3.1 is used. Thestatistic

U _(i,j) ² +V _(i,j) ²

makes intuitive sense given the quadrature nature of the offset up-downcounters and the similarities with non-coherent radio frequency carrierenvelope detection. However, it may be shown that the expected value ofthis square-law statistic depends upon the background flux, which wouldresult in a bias in the estimation of the beacon position in thepresence of nonuniform background, as well as degradation in signaldetection performance. This bias is removed by subtracting twice theup-count output of each pixel from the square-law statistic, leading tothe modified square-law statistic

W _(i,j) =U _(i,j) ² +V _(i,j) ²−2S _(i,j)  (17)

E[W _(i,j)|ε,λ_(s) _(i,j) ,λ_(b) _(i,j) ]=λ_(s) _(i,j) ² T _(int)²(1−2ε+2ε²).  (18)

The variance is more complicated; however, averaging over the fractionaltiming offset ε, we obtain the expression which is a function of higherorder powers of the signal as well as background, due to the squaringoperation. Further information on signal detection and acquisition isfound on pages 7-8 of U.S. Provisional Patent Application No.62/300,240, filed Feb. 26, 2016, by Kenneth S. Andrews, William H. Farr,Andre Wong, and Meera Srinivasan, entitled “OPTICAL BEACON ACQUISITIONAND TRACKING USING UP/DOWN COUNTING ALGORITHMS” and cross-referencedabove.

During uplink beacon detection and acquisition, the spacecraft pointinguncertainty region is scanned to detect the signal. Using an estimate ofthe background obtained beforehand to compute the threshold, the signaldetection statistic Z_(k) is calculated for all of the subwindows of thearray. The size and number of subwindows may be adjusted based upon thebackground level, required performance, and flight electronicsprocessing capability. A simple alternative algorithm consists ofcalculating the modified square-law statistic for each individual pixel,finding the maximum, and comparing that value to the threshold γcalculated for a single pixel.

7. Centroiding

In order to estimate the location of the uplink signal for the purposeof pointing and tracking, a centroid estimate is used in which theweight used for each pixel may be either the up-count statisticS_(i,j)(k) or the modified square-law up-down counter statisticW_(i,j)(k), where the indices i, j, and k, indicate the pixel in thei^(th) row and j^(th) column of the particular subwindow k. The uplinkcentroid estimate

{circumflex over (C)}(k)=({circumflex over (x)}( k ),{circumflex over(y)}(k)),

using the modified square-law up-down counter statistic, is calculatedas

$\begin{matrix}{{\hat{x}(k)} = \frac{\sum\limits_{j = 0}^{N_{cols} - 1}{\left( {j + 0.5} \right){\sum\limits_{i = 0}^{N_{rows} - 1}{W_{i,j}(k)}}}}{\sum\limits_{j = 0}^{N_{col} - 1}{\sum\limits_{i = 0}^{N_{rows} - 1}{W_{i,j}(k)}}}} & (24) \\{{\hat{y}(k)} = \frac{\sum\limits_{i = 0}^{N_{rows} - 1}{\left( {i + 0.5} \right){\sum\limits_{j = 0}^{N_{col} - 1}{W_{i,j}(k)}}}}{\sum\limits_{j = 0}^{N_{col} - 1}{\sum\limits_{i = 0}^{N_{rows} - 1}{W_{i,j}(k)}}}} & \;\end{matrix}$

where N_(col) and N_(rows) are the number of columns and rows in thesubwindow, and{circumflex over (x)} and ŷare given in pixel units. The conventional centroid estimate using theup-counts may be obtained by substituting the statistics S_(i,j)(k) forW_(i,j)(k) in (24). The performance of the centroid estimate may beevaluated via simulation and quantified as centroiding bias and jitter(RMS error).

Once the uplink beacon has been detected, the centroid formula in (24)is calculated over a specified size subwindow in order to steer theplatform to move the beacon to the pixel crosshairs of a designatedtracking region. At that point, the subwindow size is reduced toeliminate background, and the beacon centroid estimate is used tomaintain the uplink beam position so that temporal synchronization anddata demodulation may commence. The downlink transmitter may then beturned on and pointed using the uplink beacon reference position andephemeris data provided by the spacecraft. The downlink pointing inconfirmed by splitting off a portion of the transmitted beam power to beretro-reflected onto the detector array so that its position may also beestimated. As the downlink modulation occurs at a much higher rate thanmay be processed by the flight detector readout electronics, up-downcounting background subtraction cannot be used for downlink detection.Instead, the conventional centroid estimate using the up-counts is usedto estimate and track the downlink spot position. As the downlink signalis expected to be in a location of the detector array separated from theuplink beacon and the Earth, the inventors do not expect in-bandbackground to interfere as much with its tracking. Furthermore, a degreeof control over how much power may be diverted into the retro-reflecteddownlink is available, and it may be adjusted to achieve the fidelity ofdownlink tracking that we require.

8. Parameter Estimation

Estimates of certain signal and channel parameters are typicallynecessary for accurate data recovery. Slot and symbol synchronizationutilizes estimates of the symbol timing offset δ in an error-trackingtiming recovery loop. As forward error correction is applied to theuplink command data, the decoding of that data requires an estimate ofthe mean signal and background flux rates in order to form decoderlog-likelihood ratios. [8] Once in uplink tracking mode, the beaconsignal is restricted to a small tracking subwindow ω_(t), and theprocess of uplink timing and data recovery may proceed. The up-downcounter values over the pixels in ω_(t) must be added in order tocollect the combined signal power which is split over at least fourpixels. The summed up-down counter statistics are given byU_(t)=Σ_(i,jεω) _(t) U_(i,j) and V_(t)=Σ_(i,jεω) _(t) V_(i,j).Examination of the up-down counter expected values in (11) and (12)leads to the following plausible estimates for the symbol timing offsetδ and the mean signal counts per symbol K_(s)=4λ_(s)T_(slot):

$\begin{matrix}{\hat{\delta} = \left\{ \begin{matrix}\frac{V_{t}}{U_{t} + V_{t}} & {{U_{t} > 0},{V_{t} > 0}} \\{1 + \frac{U_{t}}{U_{t} - V_{t}}} & {{U_{t} < 0},{V_{t} > 0}} \\{2 + \frac{V_{t}}{U_{t} + V_{t}}} & {{U_{t} < 0},{V_{t} < 0}} \\{3 + \frac{U_{t}}{U_{t} - V_{t}}} & {{U_{t} > 0},{V_{t} < 0}}\end{matrix} \right.} & (25) \\{{\hat{K}}_{s} = \left\{ \begin{matrix}{\frac{1}{N}\left( {U_{t} + V_{t}} \right)} & {U_{t} > V_{t} > 0} \\{\frac{1}{N}\left( {{- U_{t}} + V_{t}} \right)} & {{U_{t} < 0},{V_{t} > 0}} \\{\frac{1}{N}\left( {{- U_{t}} - V_{t}} \right)} & {{U_{t} < 0},{V_{t} < 0}} \\{\frac{1}{N}\left( {U_{t} - V_{t}} \right)} & {{U_{t} > 0},{V_{t} < 0}}\end{matrix} \right.} & (26)\end{matrix}$

where N is the number of symbols or beacon cycles over which the up-downcounters are collected.

9. Performance Results

Simulation

Performance of the signal detection, centroiding, and parameterestimation algorithms was evaluated through a combination of analysis,computer simulation, and laboratory testing. Of these methods, computersimulation provides the most flexible method of parametricallypredicting performance. Toward these ends, a Matlab simulation wasdeveloped encompassing uplink signal modulation, Earth and stray lightmodeling, flight detector statistical output modeling, and signalprocessing algorithms, as shown in FIG. 13.

FIG. 13 shows a block diagram of Matlab uplink signal processingsimulation comprising a detector array/ROIC model 1300 receiving inputfrom link parameters 1302, uplink modulated beacon irradiance andposition 1304, earth model 1306, stray light 1308, and downlink beamirradiance and position 1310. The detector array ROIC model 1300 outputsto signal counters 1312 and the signal counters 1312 output toalgorithms comprising a detection algorithm 1314 (outputting Pfa, Pmd),centroid algorithms 1316 (outputting bias and jitter), and parameterestimates 1318 (RMS error). The algorithms receive input from receiveralgorithm parameters 1320.

The simulation includes an ideal two-dimensional Gaussian approximationto the Airy signal intensity pattern on the detector array, as well as anumerically integrated model of the Earth whose shape can be adjustedbased upon the angle of illumination from the Sun. The detector pixelsare assumed to collect the incident photons over the full extent of thearray, but a spatial model of the lenslet array is not included. In theworst case, the spacecraft is at far range, leading to very low signalflux at the spacecraft, and the Earth is fully illuminated from thespacecraft point-of-view. A case in which the uplink beacon is 5 kWaverage power and the spacecraft is 2.7 AU from the Earth is modelled,leading to a detected beacon signal count rate of approximately 25,000counts/sec/pixel (limited to about four pixels), and a detected Earthbackground count rate of approximately 100,000 counts/sec/pixel,assuming the parameters listed in Table 1.

The performance of the signal detection algorithm and decision statisticmay be obtained by testing the probability of false alarm andprobability of missed detection via a Monte Carlo simulation in which asignal is repeatedly placed either within a subwindow or outside of it,and the resulting decision statistic is computed and then compared tothe appropriate threshold given in (22). FIG. 14A-14B shows theprobability of missed detection using the modified square-law statisticas a function of integration time and background flux for probability offalse alarm set to 10⁻⁶ and 10⁻³, for the link parameters listed inTable 1. We observe from these plots that an integration time on theorder of 20 ms per search step is sufficient to reliably detect thebeacon when the background flux (dominated by Earth radiance) is on theorder of 10⁷ detected counts/sec. Once the background flux startsexceeding this level, longer integration times are needed, increasingthe overall acquisition time. The effect of blocking was not consideredin these particular simulations of the missed detection probability.

TABLE 1 Parameters used in uplink simulation and testing Parameter valueuplink wavelength 1.064 μm range 2.7 AU average beacon power 5 kW beaconirradiance 4.6 pW/m²) Earth radiance 0.0087 pW/(cm² · sr · μm) straylight radiance 8.7 × 10⁻⁵ pW/(cm² · sr · μm) modulation extinction ratio20 dB beacon/command channel slot width 65.536 μsec aperture diameter 22cm filter bandwidth 1 nm receiver optical loss 3.24 dB detector fillfactor 75% array size 32 × 32 pixel field-of-view 250 μrad detectionefficiency 40% detector pixel dark flux 8000 counts/sec/pixel detectorblocking time 2.048 μsec

Performance evaluation of uplink beacon centroiding is critical, as theerror in knowledge of the beacon position is a dominant contributor tothe downlink pointing error and, consequently, the downlink losses. Thecentroid error consists of both bias and jitter components, which wemeasure through Monte Carlo simulation under a variety of conditions,including different beacon positions within ±0.5 pixel from thecrosshairs of a 4×4 centroiding subwindow located at the center of thedetector array. The beacon is offset from the center of the full Earth,so that the Earth center-of-mass is not coincident with the beaconlocation. FIG. 15A-15B shows the expected values of the modifiedsquare-law centroid algorithm root-sum-square (RSS) bias and jitter as afunction of the X and Y beacon positions, in the absence of blocking. Wesee that the RSS bias is symmetric and that its expected value is zeroat the crosshairs and centers of pixels, due to the spatial symmetry ofthe signal model. Conversely, the RSS jitter is maximum at the pixelcrosshairs. The jitter is also not symmetric because the beacon isoffset from the Earth center, whose flux contributes to the centroidjitter via the modified square-law statistic variance, but not to thecentroid bias which depends upon the expected value of the modifiedsquare-law statistic.

In FIG. 16A-16B, uplink beacon centroiding simulation results are shownwhen the beacon is positioned at the pixel crosshairs, with and withoutdetector blocking, as a function of integration time (the time overwhich the centroiding statistics are collected). The Gaussian blockingmodel described in Section 2.2 is implemented in the simulation. Whenthe performance of the modified square-law centroid is compared withthat of the conventional up-count centroid. It is again seen that themodified square-law centroid outperforms the up-count centroid in termsof bias but not jitter. It is also seen that for this case blockingaffects the modified square-law centroid more than the up-countcentroid, increasing the error terms by 0.1 to 0.2 μrad at lowerintegration times. However, even with blocking, the total centroid error(bias plus jitter) using the modified square-law statistic is within 1μrad for integration times longer than about 17 ms (less than 60 Hzupdate rates).

The accuracy of the symbol timing offset and signal count estimatesgiven in (25) and (26) was also evaluated via simulation as a functionof integration time for the parameters in Table 1. A typicalrule-of-thumb for minimal decoder loss is to achieve an RMS timing errorof less than 0.1 slot. FIG. 17A-17B shows that this level of error iseasily achieved at integration times of greater than 10 ms for thenominal background radiance level. When the background radiance isincreased by an order of magnitude, this level can be achieved byincreasing the integration time. Similarly, under nominal conditions,the mean signal count may be estimated to a less than 10% error forintegration times of 20 ms or longer.

10. Laboratory Tests

The DSOC photon counting camera testbed is designed to emulate thechannel conditions under which the flight terminal is expected tooperate. By mimicking the signal and detector configuration, the testbedprovides parametric test capability of both the photon counting detectorarray and the signal processing algorithms described here. The testbedprojects a modulated 1064 nm laser simulating the DSOC uplink laser, aCW 1550 laser simulating the DSOC downlink laser, and a white lightbackground source onto the photon counting camera (see block diagram inFIG. 13). A commercial photon counting detector (PCD) array hybridizedto a readout integrated circuit [6] was used in the results presentedhere. The photon counting array consists of 1024 pixels arranged in a32×32 grid with 100 μm spacing, each pixel having a circular 16 μmdiameter photosensitive region.

Between both the 1064 nm and 1550 nm laser sources and the photoncounting camera are optics designed to provide adjustability to theprojected laser spots. The optics are designed to project a spot size ofapproximately 4 pixels (2×2) for a 100 nm pixel pitch design for thephoton counting camera to emulate the design expectations for the DSOCflight terminal. These optics may be changed as needed to adjust thespot size. Filter wheels with neutral density attenuators provideorder-of-magnitude control of flux levels from each of the sources,while fine tuning of flux levels is achieved by adjusting theconnections of the laser fiber coupling. Kinematically mounted foldmirrors allow for relative spot positioning between the two lasers onthe PCC image plane.

The 1550 nm laser is a continuous source, while the 1064 nm laser isconnected to a modulator. The modulator is driven by a set of FPGA-basedelectronics which implements the uplink beacon signal format describedin Section 2.1. The background source contains a variable output LED foradjusting flux levels. Additionally, a pinhole can be placed in front ofthe LED source in order to project an Earth-sized spot on the imageplane. A dichroic combines the background earth projection and the 1064nm laser source as would be seen by the DSOC flight terminal duringoperation. Finally, the detector array is mounted to acomputer-controlled X-Y positioner stage which provides sub-pixeltranslation, needed to investigate the effects of spatialnonuniformities in the detector array on the performance of thealgorithms as well as intrapixel effects.

The photon counting camera used in the laboratory has a 32×32 array ofavalanche photo-diodes (APDs), co-packaged with a read-out integratedcircuit (ROIC). The ROIC manages the biasing and quenching requirementsof the APDs, and records photon arrival times at each of the pixels to 1nsec accuracy. For the low data rates used in this experiment, suchtiming accuracy is not necessary, so a second set of ROIC outputs isused that reports photon arrivals over approximately 2 μsec intervals.

These data are transferred from the ROIC to a Field Programmable GateArray (FPGA), where the initial data reduction is performed. Thehigh-speed portions of four algorithms are implemented in Verilog: twofor performing centroiding on the modulated uplink beacon (one at anunknown location anywhere on the array, and the second at a knownlocation), one for demodulating the received uplink data, and one forcentroiding on the downlink laser signal.

During uplink beacon acquisition, the received laser spot may appearanywhere on the detector array. Hence, the modified square-law statisticgiven by equations 8 through 10 and 17 is computed at a 60 Hz rate forevery pixel in the array. In the hope that the beacon centroid liesclose to the pixel for which W_(i,j) is greatest, this pixel is taken asthe center of a 3×3 window, and the centroid is calculated using 24. Forconvenience in implementation, the FPGA computes the numerators and thecommon denominator of these fractions in 32-bit integer arithmetic, andpasses these values to a microprocessor, where the division operationsare performed by C-language software. It is also the responsibility ofthe software to validate the centroid estimate based on the magnitude ofthe centroid denominator, and on the consistency of the centroidestimate over time.

After beacon acquisition, better performance of the centroid algorithmcan be achieved by placing the beacon spot near the crosshairs betweenfour pixels. The advantages are several. First, as shown in FIG. 12, thealgorithm is most sensitive to spot motion on the pixel boundaries, duein part to the algorithm itself and in part to the geometry of thephotosensitive area of each pixel. Second, this spot placement allowsthe use of a 2×2 window instead of a 3×3 window, thus collecting fewerbackground photons. Third, it permits selecting a particular 2×2 window,where the pixels have particularly good detection efficiency and lowdark count rate. For these reasons, a second beacon centroidingalgorithm is implemented in the FPGA, and it performs the samecentroiding calculations in 17 and 24, but over a specific 2×2 window asspecified by the microprocessor.

Rather than pointing the downlink laser directly at the location of theuplink beacon, a point-ahead angle is included to allow for motionduring the round-trip light time. To permit closed-loop control of thispoint-ahead angle, a small portion of the downlink laser signal isredirected onto the APD array, and the centroid of this spot is computedas well. The modulation rate of the downlink laser is far faster than 2μsec rate at which the APD is monitored, and so it appears as anunmodulated spot. Hence, the downlink centroiding algorithm can only usethe sum statistic of 10. During downlink transmission, the uplink beaconspot is driven to a pixel crosshair, and the point-ahead angle is known,and so the location of the downlink laser spot is also known to theopen-loop accuracy of the point-ahead mirror. Thus, the downlinkcentroiding algorithm uses a 3×3 window at a location specified by theprocessor.

Finally, the optical uplink data is also detected by the PCC anddemodulated by the FPGA. As described above, detected counts from thePPM-modulated signal are summed over the four pixels in the specified2×2 tracking window. Slot timing is determined by a tracking loop thatconsists of an error function related to the symbol timing offsetestimate given in 25 and a low-pass filter. In this way, the FPGAreports the number of photons detected in the two PPM slots of eachsymbol. These slot statistics are simply stored for later analysis andprocessing in this implementation. In a future implementation, it isintended that they would be drive a soft-symbol decoder for theunderlying error correcting code.

For the laboratory test results presented here, the beacon laser spotwas displaced from the center of the emulated Earth by approximately onepixel in each of the X and Y dimensions, representing a case in whichthe uplink transmitter station location is offset from the center of thefull Earth when seen from the spacecraft. FIG. 20A-20B shows imagescaptured from a single 60 Hz output from the FPGA processing describedabove. FIG. 20A is the up-count output, showing the Earth image with thebeacon spot, the downlink spot, and other variations in pixel outputlevels due to dark counts, stray light, etc. (including a “hot” pixel).FIG. 20B is the modified square-law output, which has effectivelymitigated the background and reveals only the 2×2 uplink beacon.

FIG. 18 shows a laboratory photon counting detector array according toone or more embodiments, comprising FPGA electronics 1800, lasermodulator 1802, laser source 1804 (uplink, 1064 nm wavelength), filterwheel 1806, beam combiner kinematic mirror mount (position adjustment)1810, continuous wave CW laser source 1812 for the downlink (1550 nmwavelength), photon counting camera 1814, FPGA signal processing 1816,data collection personal computer (PC) 1818, aperture 1820, X-Ytranslation stage 1822, and dimmable LED source 1824 representing theearth.

Using the setup shown in FIG. 18 and the spatial configuration shown inFIG. 20, the uplink and down-link centroids were calculated withdifferent levels of Earth flux, ranging from zero up to 240,000 detectedcounts/sec/pixel. The uplink beacon flux and downlink flux were heldconstant at approximately 100,000 counts/sec and 200,000 counts/sec,respectively. FIG. 21A-21B shows the mean and RMS jitter values for theup-link centroid estimates as a function of the estimated Earth flux,for centroid calculations using the modified square-law statistics andthe up-count statistics. From FIG. 21A, we see that the mean estimatedposition from the up-count centroid shifts in value as the Earth fluxincreases, while the modified square-law centroid position remainsconstant. This demonstrates that the modified square-law centroidestimate is not biased by the Earth background. FIG. 21B shows the RMSjitter as a function of Earth flux. The up-count centroid jitterdecreases with Earth background due to the increase in total flux, whilethe modified square-law centroid jitter increases. Simulations were runfor the conditions under which these lab tests were conducted. TheGaussian blocking model was used in the simulation when the Earth fluxexceeded 1.5×10⁵ counts/sec/pixel, while the Poisson model was used inthe lower flux cases. The simulated performance shows reasonablecorrespondence with the measured results, which demonstrate the impactof blocking upon centroid jitter. Plots of downlink centroid results arenot shown here, but were measured to be stable and constant, with thejitter not exceeding 0.1 μrad.

Further information on one or more embodiments of the photon countingdetector array can be found in reference [10].

Process Steps

Transmitter

FIG. 22 illustrates a method of fabricating a transmitter.

Block 2200 represents connecting a fiber optic coupler to a polarizationmaintaining optical fiber. The fiber optic coupler comprises a firstcoupler input, a second coupler input, and a coupler output. The coupleroutput is coupled to the optical fiber comprising a polarizationmaintaining optical fiber having a slow axis and a fast axis.

Block 2202 represents connecting a first laser to the first couplerinput, wherein a first polarization axis of light emitted from the firstgated laser is aligned to the slow axis. The step further comprisesconnecting a second laser to the second coupler input, wherein a secondpolarization axis of the second laser is aligned to the fast axis.

Block 2204 represents obtaining/assembling a circuit comprising firstinput, a second input, a third input, a fourth input, a first output anda second output.

Block 2206 represents the end result, a transmitter, e.g., asillustrated in FIG. 4. In one or more embodiments, the first laser andthe second laser are gain switched diode lasers.

In one or more embodiments, the transmitter emits short laser pulses, orpulse widths are reduced. In one or more embodiments, the transmittedsignal having short/reduced pulse widths aids the receiver to detect thetransmitted signal over the noise.

Receiver

FIG. 23 represents a method of fabricating and operating a receiver.

Block 2300 represents assembling/obtaining a circuit comprising a firstphotodiode connected to a non-inverting output; and a second photodiodeconnected to an inverter, wherein the inverter comprises an invertingoutput.

In one or more embodiments, the photodiodes comprise Geiger modeavalanche photodiodes.

In one embodiment, the first photodiode connected to a first transformerhaving a first input winding inductively coupled to first outputwinding, the first output winding connected to the non-inverting output;and the second photodiode connected to a second transformer having asecond input winding inductively coupled to a second output winding, thesecond output winding having an inverting output connected to thenon-inverting output. In one or more embodiments, the transformers aresubstantially similar/the same. In one or more embodiments, thetransformers have a similar/same number of windings.

The step further comprise providing a bias input resistively coupled tothe photodiodes; and providing an over-biasing input capacitivelycoupled to the photodiodes. In one or more embodiments, the photodiodesare biased in parallel from a common voltage source through independentcurrent limiting resistors, the bias inputs are connected to thephotodiode's cathodes, the bias voltages are below the breakdownvoltages, the overbias voltage comprises pulses from a common pulsedsource applied to the photodiodes through parallel AC couplingcapacitors, the windings each having a first terminal (1) and a secondterminal (2) the first input winding having its first terminal connectedto the first photodiode's anode and its second terminal grounded, thesecond input winding having its first terminal connected to the firstphotodiode's anode and its second terminal grounded, the first outputwinding having its first terminal grounded and its second terminalconnected to the non-inverting output, the second output winding havingits first terminal connected to the inverting output and its secondterminal grounded, a photon detection event on the first photodiodecreates a positive going pulse, whereas a photon detection event on thesecond photodiode creates a negative going pulse, and simultaneousphoton detection events on each of the photodiodes are at leastpartially canceled, creating no detectable output at the output.

A driver circuit may be provided to drive the gain switched laser diodesusing the output from the logic circuit.

The circuit output is connected to the non-inverting output and theinverting output.

In one or more embodiments, an array of pixels is provided, wherein eachpixel comprises the first photodiode and the second photodiode.

Block 2302 represents coupling a polarizing beamsplitter to thephotodiodes, the polarizing beamsplitter splitting the firstelectromagnetic signal and the second electromagnetic signal emittedfrom a single laser (e.g., in a transmitter). The first photodiode iscoupled to a first polarizer transmitting the first electromagneticsignal to the first photodiode having a first polarization. The secondphotodiode is coupled to a second polarizer transmitting the secondelectromagnetic signal to the first photodiode having a secondpolarization. In one or more embodiments, the first electromagneticsignal comprises a data signal representing the first binary state in adata stream, the second electromagnetic signal comprises a data signalrepresenting the second binary state in a data stream, and the datastream comprising the first binary state and the second binary state isextracted from the output of the receiver.

Block 2304 represents connecting a computer or processor for extractingthe data stream from the output.

Block 2306 represents the end result, a receiver. In one or moreembodiments, the overbias voltage comprises pulses having a repetitionrate of the electromagnetic signals emitted from the laser. A requiredphase alignment between that rate and the timing of the gates of thedetectors is provided. One embodiment sweeps through all phases until asignal is detected.

In one or more embodiments, the transmitted signal is obtained byperforming a time domain correlation of the received signal (e.g.,Fourier transform) and selecting the signal that is above a certainthreshold.

In one or more embodiments, the receiver is connected in an opticalcommunications data link comprising a transmitter (including, but notlimited to, a transmitter as described herein) and the receiverreceiving the electromagnetic signals from the transmitter.

Counting Detector

FIG. 24 illustrates a method of fabricating a camera.

Block 2400 represents obtaining an array of imaging pixels.

Block 2402 represents fabricating or obtaining a circuit/processor(e.g., field programmable gate array FPGA) and connecting thecircuit/processor to each of the pixels.

Each of the pixels detect one or more photons received on the pixel whena first clock signal or a second clock signal are applied to the pixels.The clock signals have a rate that is a multiple of a transmission rateof a beacon signal transmitted from a source. The first clock signal isphase shifted (e.g., by 90 degrees or other phase shift) with respect tothe second clock signal, and the first and second clock signals eachcomprise a first time slot and a second time slot immediately after thefirst time slot, the first and second time slots having equal timeduration. The duration is substantially similar to an average on time ofthe beacon signal.

The circuit/processor, for each pixel:

-   -   counts a first number of photons detected by the pixel in the        first time slot of the first clock signal,    -   subtracts, from the first number, a second number of the photons        detected by the pixel in the second time slot of the first clock        signal, obtaining a first statistic U,    -   counts a third number of photons detected by the pixel in the        first time slot of the second clock signal,    -   subtracts, from the third number, a fourth number of the photons        detected by the pixel in the second time slot of the second        clock signal, obtaining a second statistic V,    -   sums the number of photons detected in the first time slot of        the first clock signal, the second time slot of the first clock        signal, the first time slot of the second clock signal, and the        second time slot of the second clock signal, obtaining a third        statistic S,    -   determines the statistic W=U²+V²−S,    -   compares W for each pixel and selects the pixel having the        highest W as a selected pixel, and    -   associates the selected pixel with one or more image pixels in        an image generated by the camera, and    -   identifies a location of the source as being in the one or more        image pixels.

FIG. 25 illustrate the end result, a camera comprising an arrayconnected to a computer or FPGA.

Block 2404 represents connecting the camera in a free space opticalcommunications link communicating the beacon signal between a firststation comprising the camera and a second station comprising a lasertransmitting the beacon signal. In one or more embodiments, the firststation comprises a satellite and the second station is located onearth. In one or more embodiments, the beacon signal and the clockfrequency are at different frequencies to account for the Doppler shiftcaused by ephemeris variance as the satellite moves. In one or moreembodiments, the first station and second station are located on earthand separated by at least 20 km and the beacon signal can be detectedthrough obscurants such as fog and cloud. The second station and/or thefirst station comprises a transmitter and receiver, including, but notlimited to, transmitters and receivers described herein.

The optical data links described herein can transmit wavelengthsincluding, but not limited to, optical, visible, ultraviolet, infrared,or midinfrared wavelengths. For example, the lasers in the transmitterscan transmit electromagnetic radiation having a wavelength in a rangefrom ultraviolet wavelengths up to a wavelength of 20 micrometers. Thereceivers can also receive and detect the electromagnetic radiation inthe range from ultraviolet to mid-infrared.

In one or more embodiments, the incoming transmitted signal can bespread over the pixels in the array so that each pixel can measure thenumber of photons that are incident. In one or more embodiments, thesignal intensity is reduced such that the array can detect 0.1 photonsper pulse.

Processing Environment

FIG. 26 illustrates a system that is coupled to the camera, transmitter,or receivers 2630 described herein, according to one or moreembodiments, in order to achieve the processing/algorithm functionsdescribed herein. The computer 2602 comprises a processor 2604 and amemory, such as random access memory (RAM) 2606. In embodimentsrequiring a human interface, the computer 2602 is operatively coupled toa display 2622, which presents images such as windows to the user on agraphical user interface 2618B. The computer 2602 may be coupled toother devices, such as a keyboard 2614, a mouse device 2616, a printer,etc. Of course, those skilled in the art will recognize that anycombination of the above components, or any number of differentcomponents, peripherals, and other devices, may be used with thecomputer 2602.

Generally, the computer 2602 operates under control of an operatingsystem 2608 stored in the memory 2606, and interfaces with the user toaccept inputs and commands and to present results through a graphicaluser interface (GUI) module 2618A. Although the GUI module 2618B isdepicted as a separate module, the instructions performing the GUIfunctions can be resident or distributed in the operating system 2608,the computer program 2610, or implemented with special purpose memoryand processors. The computer 2602 also implements a compiler 2612 whichallows an application program 2610 written in a programming languagesuch as Java, C++, C#, or other language to be translated into processor2604 readable code. After completion, the application 2610 accesses andmanipulates data stored in the memory 2606 of the computer 2602 usingthe relationships and logic that was generated using the compiler 2612.Analogous results can be accomplished with field programmable gatearrays (FPGAs) or other circuits. The computer 2602 also optionallycomprises an external communication device such as a modem, satellitelink, Ethernet card, or other device for communicating with othercomputers.

In one embodiment, instructions implementing the operating system 2608,the computer program 2610, and the compiler 2612 are tangibly embodiedin a computer-readable medium, e.g., data storage device 2620, whichcould include one or more fixed or removable data storage devices, suchas a zip drive, floppy disc drive 2624, hard drive, CD-ROM drive, tapedrive, etc. Further, the operating system 2608 and the computer program2610 are comprised of instructions which, when read and executed by thecomputer 2602, causes the computer 2602 to perform the operations hereindescribed. Computer program 2610 and/or operating instructions may alsobe tangibly embodied in memory 2606, thereby making a computer programproduct or article of manufacture. As such, the terms “article ofmanufacture,” “program storage device” and “computer program product” asused herein are intended to encompass a computer program accessible fromany computer readable device or media.

It is understood that the foregoing embodiment of the computer systemincludes peripherals (e.g. display 2622, GUI module 2618A, GUI 2618,mouse device 2619, keyboard 2614, printer 2628 or compiler 2612) thatmay be useful in some applications but not others.

Those skilled in the art will recognize many modifications may be madeto this configuration without departing from the scope of the presentdisclosure. For example, those skilled in the art will recognize thatany combination of the above components, or any number of differentcomponents, peripherals, and other devices, may be used.

REFERENCES

The following references are incorporated by reference herein.

-   [1] Farr, W., Regehr, M., Wright, M., Sheldon, D., Sahasrabudhe, A.,    Gin, J., and Nguyen, D., “Overview and design of the DOT flight    laser transceiver,” in [JPL Interplanetary Network Progress Report],    42-185 (May 2011).-   [2] Quirk, K. J., Gin, J., and Srinivasan, M., “Optical ppm    synchronization for photon counting receivers,” in [IEEE Military    Communications Conference, MILCOM], 1-7 (November 2008).-   [3] Farr, W., Sburlan, S., Sahasrabudhe, A., and Birnbaum, K. M.,    “Deep space acquisition and tracking with single photon detector    arrays,” in [2011 International Conference on Space Optical Systems    and Applications (ICSOS)], 117-121 (May 2011).-   [4] Cova, S., Ghioni, M., Lacaita, A., Samori, C., and Zappa, F.,    “Avalanche photodiodes and quenching circuits for single-photon    detection,” Appl. Opt. 35, 1956-1976 (April 1996).-   [5] Itzler, M. A., Entwistle, M., Krishnamachari, U., Owens, M.,    Jiang, X., Slomkowski, K., and Rangwala, S., “SWIR geiger-mode apd    detectors and cameras for 3d imaging,” in [Proceedings SPIE], 9114    (June 2014).-   [6] Frechette, J., Grossmann, P. J., Busacker, D. E., Jordy, G. J.,    Duerr, E. K., McIntosh, K. A., Oakley, D. C., Bailey, R. J.,    Ruff, A. C., Brattain, M. A., Funk, J. E., MacDonald, J. G., and    Verghese, S., “Readout circuitry for continuous high-rate photon    detection with arrays of inp geiger-mode avalanche photodiodes,” in    [Proceedings SPIE], 8375 (May 2012).-   [7] Yu, D. F. and Fessler, J. A., “Mean and variance of photon    counting with deadtime,” in [Conference Record, 1999 IEEE Nuclear    Science Symposium], 3, 1470-1474 (1999).-   [8] Moision, B. and Hamkins, J., “Deep-space optical communications    downlink budget: Modulation and coding,” in [JPL Interplanetary    Network Progress Report], 42-154 (August 2003).-   [9] Powerpoint slides entitled Binary polarization-shift-keyed    modulation for interplanetary CubeSat optical communications, by    Michael Peng, William Farr, Michael Borden, Abhijit Biswas, and    Joseph Kovalik, SPIE-Lase 2017, Jan. 30, 2017 and manuscript    entitled binary polarization-shift-keyed modulation for    interplanetary CubeSat optical communications, by Michael Peng,    William H. Farr, Michael B. Borden, Abhijit Biswas, Joseph M.    Kovalik for use in the conference proceedings for the SPIE 2017    conference.-   [10] Meera Srinivasan; Kenneth S. Andrews; William H. Farr and Andre    Wong “Photon counting detector array algorithms for deep space    optical communications”, Proc. SPIE 9739, Free-Space Laser    Communication and Atmospheric Propagation XXVIII, 97390X (Mar. 15,    2016); doi:10.1117/12.2217971; http://dx.doi.org/10.1117/12.2217971

CONCLUSION

This concludes the description of the preferred embodiment of thepresent invention. The foregoing description of one or more embodimentsof the invention has been presented for the purposes of illustration anddescription. It is not intended to be exhaustive or to limit theinvention to the precise form disclosed. Many modifications andvariations are possible in light of the above teaching. It is intendedthat the scope of the invention be limited not by this detaileddescription, but rather by the claims appended hereto.

What is claimed is:
 1. A transmitter, comprising: a polarizationmaintaining optical fiber having a slow axis and a fast axis; a fiberoptic coupler comprising a first coupler input, a second coupler input,and a coupler output, wherein the coupler output is coupled to theoptical fiber; first laser connected to the first coupler input, whereina first polarization axis of light emitted from the first laser isaligned to the slow axis; a second laser connected to the second couplerinput, wherein a second polarization axis of the second laser is alignedto the fast axis; a circuit comprising first input, a second input, athird input, a fourth input, a first output and a second output,wherein: the optical fiber outputs the electromagnetic radiation havingthe first polarization axis representing a first binary state andemitted from the first laser, when the first output outputs a signalswitching the first laser on in response to the first input receiving aclock signal and the second input receiving a data signal representingthe first binary state in a data stream; and the optical fiber outputsthe electromagnetic radiation having the second polarization axisrepresenting a second binary state and emitted from the second laser,when the second output outputs a signal switching the second laser on inresponse to the third input receiving the clock signal and the fourthinput receiving a data signal representing the second binary state inthe data stream.
 2. The transmitter of claim 1, wherein the first laserand the second laser are gain switched diode lasers.
 3. The apparatus ofclaim 1, wherein the circuit comprises a logic circuit.
 4. The apparatusof claim 1, wherein the logic circuit comprises: a first AND gate havingthe first and second inputs and the first output, and the second ANDgate having the third and fourth inputs and the second output, whereinthe fourth input is an inverting input.
 5. A data link comprising thetransmitter of claim 1 and a receiver receiving the electromagneticsignals from the transmitter, the receiver comprising: a firstphotodiode connected to a non-inverting output; a second photodiodeconnected to an inverter, wherein the inverter comprises invertingoutput; a bias input resistively coupled to the photodiodes; anover-biasing input capacitively coupled to the photodiodes; an outputconnected to the non-inverting output and the inverting output; wherein:the output sums a first signal at the non-inverting output with a secondsignal at the inverting output when: the first photodiode outputs thefirst signal to the non-inverting output in response to a firstelectromagnetic signal received on the first photodiode, an overbiasingvoltage applied to the overbiasing input, and a bias voltage applied tothe bias input; and/or the inverter outputs the second signal to theinverting output, the second signal formed by inverting the photodiodesignal received from the second photodiode in response to a secondelectromagnetic signal received on the second photodiode, theoverbiasing voltage applied to the overbiasing input and the biasvoltage applied to the bias input; and the first signal at leastpartially cancels the second signal when the first photodiode receivesthe first electromagnetic signal and the second photodiode receives thesecond electromagnetic signal while the bias voltage and the overbiasvoltage are applied.
 6. A receiver, comprising: a first photodiodeconnected to a non-inverting output; a second photodiode connected to aninverter, wherein the inverter is connected to a non-inverting output; abias input resistively coupled to the photodiodes; an over-biasing inputcapacitively coupled to the photodiodes; an output connected to thenon-inverting output and the inverting output; wherein: the output sumsa first signal at the non-inverting output with a second signal at theinverting output when: the first photodiode outputs the first signal tothe non-inverting output in response to a first electromagnetic signalreceived on the first photodiode, an overbiasing voltage applied to theoverbiasing input, and a bias voltage applied to the bias input; and/orthe inverter outputs the second signal to the inverting output, thesecond signal formed by inverting the photodiode signal received fromthe second photodiode in response to a second electromagnetic signalreceived on the second photodiode, the overbiasing voltage applied tothe overbiasing input and the bias voltage applied to the bias input;and the first signal at least partially cancels the second signal whenthe first photodiode receives the first electromagnetic signal and thesecond photodiode receives the second electromagnetic signal while thebias voltage and the overbias voltage are applied.
 7. The receiver ofclaim 6, further comprising: the first photodiode connected to a firsttransformer having a first input winding inductively coupled to firstoutput winding, the first output winding connected to the non-invertingoutput; and the second photodiode connected to a second transformerhaving a second input winding inductively coupled to a second outputwinding, the second output winding having an inverting output connectedto the non-inverting output;
 8. The receiver of claim 7, wherein: thephotodiodes are biased in parallel from a common voltage source throughindependent current limiting resistors the bias inputs are connected tothe photodiode's cathodes, the bias voltages are below the breakdownvoltages, the overbias voltage comprises pulses from a common pulsedsource applied to the photodiodes through parallel AC couplingcapacitors, the windings each having a first terminal and a secondterminal, the first input winding having its first terminal connected tothe first photodiode's anode and its second terminal grounded, thesecond input winding having its first terminal connected to the firstphotodiode's anode and its second terminal grounded, the first outputwinding having its first terminal grounded and its second terminalconnected to the non-inverting output, the second output winding havingits first terminal connected to the inverting output and its secondterminal grounded, a photon detection event on the first photodiodecreates a positive going pulse, whereas a photon detection event on thesecond photodiode creates a negative going pulse, and simultaneousphoton detection events on each of the photodiodes are at leastpartially canceled, creating no detectable output at the output.
 9. Thereceiver of claim 6, wherein the photodiodes comprise Geiger modeavalanche photodiodes.
 10. The receiver of claim 6, further comprisingan array of pixels, wherein each pixel comprises the first photodiodeand the second photodiode.
 11. The receiver of claim 6, furthercomprising: a polarizing beamsplitter coupled to the photodiodes, thepolarizing beamsplitter splitting the first electromagnetic signal andthe second electromagnetic signal emitted from a single laser, wherein:the first photodiode is coupled to a first polarizer transmitting thefirst electromagnetic signal to the first photodiode having a firstpolarization; and the second photodiode is coupled to a second polarizertransmitting the second electromagnetic signal to the first photodiodehaving a second polarization.
 12. The receiver of claim 11, wherein theoverbias voltage comprises pulses having a repetition rate of theelectromagnetic signals emitted from the laser and a required phasealignment between the rate and timing of the overbias is provided. 13.The receiver of claim 6, wherein: the first electromagnetic signalcomprises a data signal representing the first binary state in a datastream, the second electromagnetic signal comprises a data signalrepresenting the second binary state in a data stream, and the datastream comprising the first binary state and the second binary state isextracted from the output of the receiver.
 14. A data link comprising atransmitter and the receiver of claim 13 receiving the electromagneticsignals from the transmitter, the transmitter, comprising: apolarization maintaining optical fiber having a slow axis and a fastaxis; a fiber optic coupler comprising a first coupler input, a secondcoupler input, and a coupler output, wherein the coupler output iscoupled to the optical fiber; first laser connected to the first couplerinput, wherein a first polarization axis of light emitted from the firstgated laser is aligned to the slow axis; a second laser connected to thesecond coupler input, wherein a second polarization axis of the secondlaser is aligned to the fast axis; a circuit comprising first input, asecond input, a third input, a fourth input, a first output and a secondoutput, wherein: the optical fiber outputs the first electromagneticsignal having the first polarization axis representing a first binarystate and emitted from the first laser, when the first output outputs asignal switching the first laser on in response to the first inputreceiving a clock signal and the second input receiving a data signalrepresenting the first binary state in a data stream; and the opticalfiber outputs the second electromagnetic signal having the secondpolarization axis representing a second binary state and emitted fromthe second laser, when the second output outputs a signal switching thesecond laser on in response to the third input receiving the clocksignal and the fourth input receiving a data signal representing thesecond binary state in the data stream.
 15. A camera, comprising: anarray of imaging pixels; and a circuit connected to each of the pixels,wherein: each of the pixels detect one or more photons received on thepixel when a first clock signal or a second clock signal are applied tothe pixels, the clock signals have a rate that is a multiple of atransmission rate of a beacon signal transmitted from a source, and thefirst clock signal is phase shifted by 90 degrees with respect to thesecond clock signal, the first and second clock signals each comprise afirst time slot and a second time slot immediately after the first timeslot, the first and second time slots having equal time duration, theduration is substantially similar to an average on time of the beaconsignal, and the circuit, for each pixel, counts a first number ofphotons detected by the pixel in the first time slot of the first clocksignal, subtracts, from the first number, a second number of the photonsdetected by the pixel in the second time slot of the first clock signal,obtaining a first statistic U, counts a third number of photons detectedby the pixel in the first time slot of the second clock signal,subtracts, from the third number, a fourth number of the photonsdetected by the pixel in the second time slot of the second clocksignal, obtaining a second statistic V, sums the number of photonsdetected in the first time slot of the first clock signal, the secondtime slot of the first clock signal, the first time slot of the secondclock signal, and the second time slot of the second clock signal,obtaining a third statistic S, determines the statistic W=U²+V²−S,compares W for each pixel and selects the pixel having the highest W asa selected pixel, and associates the selected pixel with one or moreimage pixels in an image generated by the camera, and identifies alocation of the source as being in the one or more image pixels.
 16. Afree space optical communications link communicating the beacon signalbetween a first station comprising the camera of claim 15 and a secondstation comprising a laser transmitting the beacon signal.
 17. The linkof claim 16, wherein: the first station comprises a satellite and thesecond station is located on earth, and the beacon signal and the clocksignal are at different frequencies to account for the Doppler shiftcaused by ephemeris variance as the satellite moves.
 18. The link ofclaim 16, wherein the first station and second station are located onearth and separated by at least 20 km.
 19. The link of claim 16, whereinthe second station comprises a transmitter, the transmitter comprising:a polarization maintaining optical fiber having a slow axis and a fastaxis; a fiber optic coupler comprising a first coupler input, a secondcoupler input, and a coupler output, wherein the coupler output iscoupled to the optical fiber; first laser connected to the first couplerinput, wherein a first polarization axis of light emitted from the firstgated laser is aligned to the slow axis; a second laser connected to thesecond coupler input, wherein a second polarization axis of the secondlaser is aligned to the fast axis; a circuit comprising first input, asecond input, a third input, a fourth input, a first output and a secondoutput, wherein: the optical fiber outputs the electromagnetic radiationhaving the first polarization axis representing a first binary state andemitted from the first laser, when the first output outputs a signalswitching the first laser on in response to the first input receiving aclock signal and the second input receiving a data signal representingthe first binary state in a data stream; and the optical fiber outputsthe electromagnetic radiation having the second polarization axisrepresenting a second binary state and emitted from the second laser,when the second output outputs a signal switching the second laser on inresponse to the third input receiving the clock signal and the fourthinput receiving a data signal representing the second binary state inthe data stream.